It's unlikely to be device-specific - what's more likely is that it's history-specific, especially if you're logged into a Google account on one and not the other. Google does use what it knows about you (eg past searches) to customise your results, so that sites you've clicked through to a lot are likely to appear higher up the list than they might for other people. That's why you should always log out of your Google account before looking at where your site ranks for different terms.
Any posts I write in Arial are on my mobile phone, so please excuse typos etc. Any posts I write in Verdana are on a PC, so feel free to berate me mercilessly for any mistakes
The thing is, I wouldn't expect different data centres from two devices in the same location. What I did think however, is that results may be displayed differently for different resolutions.
Shooting from the hip I'd say that there's more space on a PC screen which would therefore be utilised differently. I'd also say that slower loading times on phones/ipads etc might effect how Google displays things.